(5n+1)(3n-6)=0

Solution for (5n+1)(3n-6)=0 equation:

Simplifying
(5n + 1)(3n + -6) = 0

Reorder the terms:
(1 + 5n)(3n + -6) = 0

Reorder the terms:
(1 + 5n)(-6 + 3n) = 0

Multiply (1 + 5n) * (-6 + 3n)
(1(-6 + 3n) + 5n * (-6 + 3n)) = 0
((-6 * 1 + 3n * 1) + 5n * (-6 + 3n)) = 0
((-6 + 3n) + 5n * (-6 + 3n)) = 0
(-6 + 3n + (-6 * 5n + 3n * 5n)) = 0
(-6 + 3n + (-30n + 15n2)) = 0

Combine like terms: 3n + -30n = -27n
(-6 + -27n + 15n2) = 0

Solving
-6 + -27n + 15n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -9n + 5n2) = 0

Factor a trinomial.
3((-1 + -5n)(2 + -1n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -5n)' equal to zero and attempt to solve:

Simplifying
-1 + -5n = 0

Solving
-1 + -5n = 0

Move all terms containing n to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -5n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5n = 0 + 1
-5n = 0 + 1

Combine like terms: 0 + 1 = 1
-5n = 1

Divide each side by '-5'.
n = -0.2

Simplifying
n = -0.2
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {-0.2, 2}